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Year 2015, Volume: 3 Issue: 2, 74 - 83, 30.10.2015

Melek Masal , Ayşe Zeynep Azak

https://doi.org/10.36753/mathenot.421334
Cited By: 8

Abstract

References

  • nces [1] Biran, L., Diferansiyel Geometri Dersleri. ˙Istanbul Universitesi Fen Fak¨ultesi Yayınları. ¨ İstanbul, 1975.
  • [2] Bishop, L. R., There is more than one way to frame a curve. American Mathematical Monthly 82 (1975), no. 3, 246-251.
  • [3] Clauvelin N., Olson W. K., Tobias I., Characterizations of the geometry and topology of DNA pictured as a discrete collection of atoms. Journal of Chemical Theory and Computation 8 (2012), no. 3, 1092-1107.
  • [4] Do Carmo, M. P., Differential Geometry of Curves and Surfaces. Prentice Hall Inc. Englewood Cliffs. New Jersey, 1976.
  • [5] Hacısalihoğlu, H. Hilmi, Diferensiyel Geometri. ˙In¨on¨u Universitesi. Fen-Edebiyat Fak¨ultesi ¨ Yayınları, Malatya, 1983.
  • [6] Han C. Y., Nonexistence of rational rotation-minimizing frames on cubic curves. Computer Aided Geometric Design 25 (2008), no. 4-5, 298-304.
  • [7] Hanson A. J., Ma H., Parallel transport approach to curve framing. Indiana University 425, vol. 11, 1995.
  • [8] Kızıltuğ S., Kaya S., Tarak¸cı O., The slant helices according to type-2 Bishop frame in ¨ Euclidean 3-space. International Journal of Pure and Applied Mathematics 85 (2013), no. 2, 211-222.
  • [9] KızıltuğS., On characterization of inextensible flows of curves according to type-2 Bishop frame in E3. Mathematical and Computational Applications 19 (2014), no. 1, 69-77.
  • [10] Shoeemake K., Animating rotation with quaternion curves. in Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, 245-254, 1985.
  • [11] Özyılmaz E., Classical differential geometry of curves according to type-2 Bishop trihedra. Mathematical and Computational Applications 16 (2011), no. 4, 858-867.
  • [12] Yılmaz S., Turgut M., A new version of Bishop frame and an application to spherical images. Journal of Mathematical Analysis and Applications 371 (2010), 764-776.

THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3

Year 2015, Volume: 3 Issue: 2, 74 - 83, 30.10.2015

Melek Masal , Ayşe Zeynep Azak

https://doi.org/10.36753/mathenot.421334
Cited By: 8

Abstract

 We have introduced the ruled surfaces which are generated from
the type-2 Bishop vectors. Then, we have calculated Gaussian curvatures,
mean curvatures and integral invariants of these surfaces. Also the fundamental
forms, geodesic curvatures, normal curvatures and geodesic torsions are
calculated and some results are obtained.

Keywords

Bishop frame ruled surfaces Euclidean 3-space

References

  • nces [1] Biran, L., Diferansiyel Geometri Dersleri. ˙Istanbul Universitesi Fen Fak¨ultesi Yayınları. ¨ İstanbul, 1975.
  • [2] Bishop, L. R., There is more than one way to frame a curve. American Mathematical Monthly 82 (1975), no. 3, 246-251.
  • [3] Clauvelin N., Olson W. K., Tobias I., Characterizations of the geometry and topology of DNA pictured as a discrete collection of atoms. Journal of Chemical Theory and Computation 8 (2012), no. 3, 1092-1107.
  • [4] Do Carmo, M. P., Differential Geometry of Curves and Surfaces. Prentice Hall Inc. Englewood Cliffs. New Jersey, 1976.
  • [5] Hacısalihoğlu, H. Hilmi, Diferensiyel Geometri. ˙In¨on¨u Universitesi. Fen-Edebiyat Fak¨ultesi ¨ Yayınları, Malatya, 1983.
  • [6] Han C. Y., Nonexistence of rational rotation-minimizing frames on cubic curves. Computer Aided Geometric Design 25 (2008), no. 4-5, 298-304.
  • [7] Hanson A. J., Ma H., Parallel transport approach to curve framing. Indiana University 425, vol. 11, 1995.
  • [8] Kızıltuğ S., Kaya S., Tarak¸cı O., The slant helices according to type-2 Bishop frame in ¨ Euclidean 3-space. International Journal of Pure and Applied Mathematics 85 (2013), no. 2, 211-222.
  • [9] KızıltuğS., On characterization of inextensible flows of curves according to type-2 Bishop frame in E3. Mathematical and Computational Applications 19 (2014), no. 1, 69-77.
  • [10] Shoeemake K., Animating rotation with quaternion curves. in Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, 245-254, 1985.
  • [11] Özyılmaz E., Classical differential geometry of curves according to type-2 Bishop trihedra. Mathematical and Computational Applications 16 (2011), no. 4, 858-867.
  • [12] Yılmaz S., Turgut M., A new version of Bishop frame and an application to spherical images. Journal of Mathematical Analysis and Applications 371 (2010), 764-776.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Melek Masal

Ayşe Zeynep Azak

Submission Date January 4, 2015
Publication Date October 30, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Masal, M., & Azak, A. Z. (2015). THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Mathematical Sciences and Applications E-Notes, 3(2), 74-83. https://doi.org/10.36753/mathenot.421334
AMA Masal M, Azak AZ. THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Math. Sci. Appl. E-Notes. October 2015;3(2):74-83. doi:10.36753/mathenot.421334
Chicago Masal, Melek, and Ayşe Zeynep Azak. “THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3”. Mathematical Sciences and Applications E-Notes 3, no. 2 (October 2015): 74-83. https://doi.org/10.36753/mathenot.421334.
EndNote Masal M, Azak AZ (October 1, 2015) THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Mathematical Sciences and Applications E-Notes 3 2 74–83.
IEEE M. Masal and A. Z. Azak, “THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 74–83, 2015, doi: 10.36753/mathenot.421334.
ISNAD Masal, Melek - Azak, Ayşe Zeynep. “THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3”. Mathematical Sciences and Applications E-Notes 3/2 (October2015), 74-83. https://doi.org/10.36753/mathenot.421334.
JAMA Masal M, Azak AZ. THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Math. Sci. Appl. E-Notes. 2015;3:74–83.
MLA Masal, Melek and Ayşe Zeynep Azak. “THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, 2015, pp. 74-83, doi:10.36753/mathenot.421334.
Vancouver Masal M, Azak AZ. THE RULED SURFACES ACCORDING TO TYPE-2 BISHOP FRAME IN THE EUCLIDEAN 3-SPACE E^3. Math. Sci. Appl. E-Notes. 2015;3(2):74-83.

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